Ex 11.3, 8
If the triangle ABC in the Question 7 above is revolved about the side 5 cm, then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained in Questions 7 and 8.
Let ABC with right angle at B.
AC will be hypotenuse, AC = 13 cm
And AB = 12 cm, BC = 5 cm
We revolve ∆ ABC about the side BC (= 5 cm)
, we get a cone as shown in the figure.
Radius = r = 12 cm,
& Height = h = 5 cm
Volume of solid so obtained = 1/3 πr2h
= (1/3×"π" ×12×12×5) cm3
= (1×"π" ×4×12×5) cm3
= 240 π cm3 .
Ratio of volume = (𝑉𝑜𝑙𝑢𝑚𝑒 𝑖𝑛 𝑄7)/(𝑉𝑜𝑙𝑢𝑚𝑒 𝑖𝑛 𝑄8)
= 100𝜋/240𝜋
= 5/12
So the ratio of volume is 5 : 12.

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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